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Analyzing gastrocnemius EMG-activity and1
sway data from quiet and perturbed standing2
Frank Borg a,∗, Maria Finell b, Ismo Hakala a and Mika Herrala a3
aUniversity of Jyvaskyla, Chydenius Institute, POB 567, FIN-67101 Karleby,4
Finland.5
bFysiofinex, Storgatan 14, FIN-68600 Jakobstad, Finland6
Abstract7
In an experiment we combined force plate measurements and surface EMG in8
studying quiet and perturbed standing, involving MS (Multiple sclerosis) and con-9
trols. The aim of this paper is to report the results thus obtained on the relation10
between filtered gastrocnemius (GA) EMG and the anterior-posterior center-of-11
pressure (A/P COP) coordinate. The main finding is the good correspondece be-12
tween A/P COP and the filtered GA EMG in the low frequency range. The EMG13
envelope was calculated using a zero-lag filter. Combining this with time shifts14
around 250 – 350 ms produced a high correlation (85.5 ± 8.4%) between the GA15
EMG envelope and the A/P COP. This EMG-COP relation was closest when us-16
ing a low cut-off frequency value around 1 Hz in calculating the EMG envelope.17
Based on this filtering procedure we estimated the average EMG-COP time shift to18
be 283 ± 43 ms between the GA-EMG envelope and A/P COP (which ”lags” be-19
hind EMG envelope). This shift is consistent with the 1 Hz cut-off and phase shift20
produced by a corresponding critically damped second order filter, and is about21
twice the corresponding twitch time. These results suggest that GA is to a large22
extent responsible for the phasic control of the anterior-posterior balance during23
quiet standing. A small difference was found between mean time shift thus obtained24
for controls (n = 4) and MS (n = 6) while sway area showed a major difference (p <25
0.01). The paper also compares three alternative filters for numerical calculation of26
the EMG-envelope. (Published as DOI: 10.1016/j.jelekin.2006.06.00)27
Key words: Center-of-pressure, Quiet standing, EMG-force relation,28
Gastrocnemius, Electromechanical Delay29
PsycINFO: 2540, 233030
∗ Corresponding author. Fax: +358 6 8294 295.Email address: [email protected] (Frank Borg).
Preprint submitted to Elsevier Science 14 March 2009
1 Introduction1
Quiet and perturbed standing have been researched by many groups over the2
years using force plates, video-based systems, EMG, and more recently also3
ultrasound. These studies have revealed that quiet standing (QS) involves4
a complex muscular dynamics in order to stabilize the basically unstable hu-5
man inverted pendulum (HIP). As has been argued i.a. by Loram et al [12, 11]6
the compliance of the tendon makes it difficult to maintain posture using a7
simple stiffness control. A constant adaptive muscle control is thus needed.8
Since during QS one is leaning a bit forward, the main stabilizing action9
in the sagittal plane is maintained by the plantar flexors (pulling the body10
backwards against gravity). This showed up in the tests by the low tibialis11
anterior (TA) activity during QS. One of our interests has been to try to12
relate the various sway-parameters used in posturology based on force plate13
data to physiological correlates; that is, to provide some physiological inter-14
pretation making the clinical use of the parameters perhaps more transparent.15
The combined force plate and EMG-measurements reveal that the anterior-16
posterior COP-coordinate and the GA-EMG are closely related (see sec. 3.3).17
This means that the A/P COP-coordinate can in part be interpreted in terms18
of the GA-activity. Naturally the whole triceps surae group is involved in the19
plantar flexor activity, but GA may have a central role for the phasic control20
of balance. The GA and A/P correlation has been observed earlier, at least21
as far back as Mulavara et al [16]. Here we show that properly (zero-phase)22
filtered GA EMG and A/P COP time series are quite similar – they are not23
merely statistically correlated – making it possible to calculate a time shift24
between them. GA-EMG and A/P COP data may therefore shed light on the25
EMG-force relation. We compare alternative methods for filtering and calcu-26
lating the EMG-envelope and how they affect the time shift. We discuss the27
interpretation of the time shift and how it might relate to the EMG-fore rela-28
tion, the visco-elastic properties of the muscle-tendon unit and the so-called29
electromechanical delay (EMD).30
Note that we have used the concept of ”time shift” instead of ”phase shift”.31
This is because the relation between the zero-lag EMG-envelope and the A/P32
COP is indeed of the form of a time shift t → t − τ , and because we have33
chosen to express the shift in terms of time instead of phase. However, using a34
causal filter, such as the critically damped filter, the ”shift” is indeed related35
to a phase shift as described below (see Eq.(9)). For the causal filter described36
below, the ”twitch time” τc is related to the ”time shift τ” by τ = 2τc in the37
low frequency bandwidth (f < fc). The twitch time corresponds to the time38
for the impulse response function to reach maximum, and is sometimes also39
referred to as ”contraction time” [21]. The calculation of shift time may be40
thus considered as a way of obtaining an estimate of the twitch time.41
2
A group of controls and an MS-group were involved in the study in order to1
have groups with clearly different balancing abilities. There seems to be only2
a relatively few published studies on the static balance and posturological pa-3
rameters for MS [see e.g. 4, 5, 6]. One could also use groups of young versus4
elderly, but in the case of MS we may have a better idea of the key physio-5
logical differences involved. MS may for instance affect the balance feedback6
mechanism through increasing the feedback delay. Indeed, the big difference7
found in sway areas between MS and controls indicates some important differ-8
ence in the feedback systems. As we find only a minor difference in the shift9
time this suggests that the time shift largely reflects the EMG-force relation.10
Besides the standard eyes open (EO) and eyes closed (EC) quiet standing11
tests we also performed a perturbation test since it was assumed to amplify12
the difference between MS and the controls.13
Finally, the findings on the EMG-force relation are of importance if one wants14
to develop models of the postural feedback system since the control system15
must be adapted to the fact that the force continues a while after the control16
signal ceases.17
2 Methods18
2.1 Participants19
Participants in the tests were adult volunteers from the local MS-society di-20
agnosed with multiple sclerosis (MS) (n = 6, 1 male/ 5 females), and neu-21
rologically intact people (office workers) (n = 4, 1 female/3 males). All the22
participants have signed their informed consent. Average body mass for the23
participants was 74.8 ± 14.2 kg, length 171.8 ± 8.5 cm, body mass index24
(BMI) 25.2 ± 3.3 (range 19.1–30.8) and age 42.5 ± 2.3 years (range 21–64).25
The average age of the MS participants (47.8 yr) was somewhat higher than26
for the controls (36.7 yr). Use of medication, eye-glasses, and similar factors27
that could affect the performance were noted. The MS participants were at the28
time highly functional although there were in some cases history of diplegia.29
Times of first diagnosis of MS were between 1 to 14 years back. Typical symp-30
toms reported were fatigue and weakness in the limbs and for this reason the31
measurement time was chosen to be 40 s instead of the usual 1 minute dura-32
tion. All except one MS-participant (participant number 6) reported weakness33
or fatigue (left or right lower limb). In terms of Kurtzke’s EDSS scale they34
were all judged to be in the 0–4.5 range. Participants are numbered 1–10 with35
1–4 comprising the controls, and 5–10 comprising the MS-group.36
3
2.2 Procedures1
The test protocol comprised 9 trials: 6 quiet standing measurements with al-2
ternating eyes open (EO) and eyes closed (EC) condition, and 3 trials with3
perturbation (and EO). We used three trials per condition for statistical rea-4
son. The same alternating EO-EC order was used for everyone for equalizing5
the conditions and for convenience. All the trials were of 40 s duration. The6
foot stance was standardized with 30 degree angle (splay) between medial7
sides of the feet and a heel-to-heel distance (clearance) of about 2 cm (the8
toes-out position also probably enhances the medial GA activity). The arms9
were held in a relaxed position on the sides. The participants were instructed10
to keep the gaze on a 7 cm × 7 cm spot (sticker) on the wall 3 m ahead.11
The perturbation test was performed using a 1.4 kg mass suspended by a wire12
over a pulley and attached to the person from the back side to the thorax13
just below the scapulae approximately at the Th9-Th10 level (this will corre-14
spond to a perturbing torque around 1.4 kg × 9.81 m s−2 × 1.1 m ≈ 15 Nm).15
About 5 seconds after commencing the measurement a thin thread connect-16
ing the weight and the wire was cut releasing the weight. The computer test17
log shows that the sessions lasted on the average around 20 minutes, while18
the preparations took typically 30 minutes per person. The participants were19
allowed to rest between the trials if needed (longest recorded rest was 5 min).20
2.3 Data acquisition21
COP-data has been obtained using a conventional force plate (Hur Co, www.22
hur.fi) with 4 × 50 kg unidirectional force transducers. The accuracy of the23
force plate is mostly affected by electronic noise. Measuring with a constant24
(calibration) weight results typically in a (Gaussian) COP-fluctuation with a25
standard deviation of 0.3 mm. Surface EMG-measurements were made with26
Noraxon Myosystem 1400 (www.noraxon.com). The amplified outputs of the27
force plate and the Myosystem (signal from its rear D25-connector whose gain28
is preset to 1000 and high-pass cut-off to 10 Hz) were connected in parallel29
to a National Instrument (www.ni.com) 16 bit AD-card model PCI-6036E in-30
terfacing an ordinary PC. According to information from Noraxon the extra31
delay due to the processing by the Myosystem is maximally around 0.5 ms.32
The measurement software was programmed using the National Instruments33
Labwindows CVI tool. EMG and force data were simultaneously sampled with34
the rate of 1000 samples per second (S/s). Force data was smoothed taking35
consecutive 10-point averages resulting in an effective sampling rate of 100 S/s.36
The force data was finally converted to COP-x (medial-lateral) and COP-y37
(anterior-posterior) coordinates and the total vertical force Fz, which were38
saved along with the raw EMG-data (1000 S/s). In six instances the perfor-39
4
mances in the perturbation tests were filmed from the right side (stationary1
video camera) in order to be able to later check whether the participants2
made some extra movements (this occurred only for two participants with a3
more progressed form of MS who occasionally showed some upper limb bal-4
ance reactions). For the EMG-measurements eight channels were used with5
the electrode locations listed in Table 1. The reference electrode was placed6
on left malleolus medialis. Surface Ag/AgCl electrodes (Ambu ”Blue Sensor7
M”, M-00-S, www.ambu.com) were arranged using the standard bipolar config-8
uration, with placements and skin preparations made in accordance with the9
SENIAM recommendations [8]. The skin-electrode impedance was checked in10
each case with a multimeter and was found to vary with the person and the11
location typically in the range of 4 to 8 kOhm (”worst” case had 80 kOhm).12
In this paper we will mainly analyze the medial gastrocnemius EMG. Tibialis13
EMG was generally quiet except in the beginning of the perturbation trials (in14
some cases) when the perturbation mass was pulling on the participant while15
the dorsal flexors resisted the tug. Multifidus (MF) was included in order to16
check its activity in the perturbation tests, the MF-signal appears however to17
be prone cardiac interference.18
2.4 Data analysis, EMG19
The collected data was analyzed using our custom C-programs (Labwindows20
CVI) and Mathcad programs (www.mathsoft.com). A zero lag filter was de-21
signed by first rectifying the EMG, then applying Fast Fourier Transformation22
(FFT), which was multiplied by a real (zero-phase) low-pass (LP) filter factor,23
and finally inverse FFT was applied in order to obtain the filtered signal s(t).24
Mathematically the filtering emg(t) → s(t) can be described by the following25
steps (a modified ”Butterworth zero-lag” low-pass filter, here denoted BW0),26
x1(t) = |emg(t)| . . . rectification (1)
x2(t) = x1(t) − 〈x1〉 . . . subtracting the mean (2)
x2(f) =∫ ∞
−∞e−i2πftx2(t)dt . . .Fourier transform (3)
x3(f) =1
1 +∣
∣
∣
f
fc
∣
∣
∣
nf· x2(f) . . .filtering (4)
s(t) =∫ ∞
−∞ei2πftx3(f)df . . . inverse Fourier transform. (5)
Here fc denotes the LP cut-off frequency. Note that the rectification step27
Eq.(1) is analogous to the rectification procedure for amplitude modulated28
(AM) radio signals which brings out the superimposed low-frequency sound29
5
signal. Similarly for EMG, the rectification enhances the low frequency content1
of the signal. Best fit (in terms of degree of maximal correlation) between A/P-2
COP and filtered GA-EMG was obtained with fc around 1 Hz and the order3
nf ≥ 2. In the calculations we adopted nf = 4. This is not a very sensitive4
parameter as long as nf ≥ 2. In order to fit filtered GA-EMG s(t) to the A/P5
COP data y(t) we have to introduce a time shift or ”delay” τ such that6
y(t) ≈ C · s(t − τ), (6)
for some ”calibration constant” C. The cross-correlation technique is a stan-7
dard method for determining time/phase shifts between signals, and the result8
for EMG-COP in terms of the time shift τ was between 250–350 ms. While the9
above filter was adopted chiefly for mathematical convenience and good cor-10
relation, there is a well known filter loosely based on a muscle model. This is11
the filter corresponding to a second order critically damped system (hereafter12
abbreviated as CRIT2) to be used in step 5 of the BW0-transformation13
h(t) =1
(
1 + i f
fc
)2 (frequency domain) (7)
h(t) =t
τ 2c
e−ttc (time domain) (8)
where t > 0 and 2πfc =1
τc
.
The form of the Eq.(7) with fc = 2.5 Hz has been suggested by Soechting and14
Roberts [19] and later evoked by Basmajian and Luca [1]. It has recently been15
used by Wrbaskic and Dowling [26] in an EMG-driven model. Soechting and16
Roberts [19] introduced the transfer function in Eq.(7) ”to provide a common17
reference for purpose of comparison”. It was based on data obtained by cyclic18
isometric contraction of biceps brachii using a force-feedback instrumentation19
setup. For frequencies f below fc = 1 Hz this filter predicts an almost constant20
delay21
∆t(f) = − 1
2πfarctan
(
2f/fc
1 − (f/fc)2
)
, (9)
which for small f is around - 1/(πfc) yielding a time shift around 318 ms with22
fc = 1 Hz (the contributions from the components f > fc are suppressed). This23
model seems thus to predict the right size of the observed time shift. A further24
observation regarding Eq.(8) is that the filter in time domain corresponds to25
taking a weighted average of the rectified EMG using a window with a size26
6
of the order of τc = 1/2πfc (≈ 159 ms). (Thus note that the twitch time is1
around half the time shift.) In fact the time-version of the BW0-filter in case2
of nf = 4 is given by3
h(t) =π√2
[
sin(√
2πfct)
sign(t) + cos(√
2πfct)]
e−√
2πfc|t|, (10)
where the sign-function is defined by sign(t) = 1 (-1) if t > 0 (t < 0), and 04
otherwise. It means that the EMG-envelope at time t0 is the weighed average5
of rectified EMG in a time interval of the order of tc = 1/(√
2πfc
)
around t0.6
For fc = 1 Hz this characteristic time becomes tc = 225 ms. This suggests one7
could use the traditional RMS-filter (note that this is centered on the time8
t + T/2),9
RMS(t) =
√
1
T
∫ T+t
temg(u)2du. (11)
Indeed, one obtains a fairly good correlation between filtered GA-EMG and10
A/P COP using RMS with the time window T ≈ 300 ms (not a critically11
sensitive value). T can be estimated theoretically by finding the square filter12
of length T which most closely fits the filter Eq.(8). This leads to T = α/2πfc13
where α ≈ 1.793 is the positive solution of the equation 1+ z + z2 = ez. (This14
equation derives from maximizing the correlation between of a T -square filter15
with the filter Eq.(8) with respect to the width T .) Thus, with fc = 1 Hz we16
obtain T = 285 ms. We have also made cursory uses of the classical EMG17
parameter defined as the EMG-turns [24]. The idea is that the turn rate may18
give a useful measure of neuro-muscular activity and thus correlate with the19
muscular force. In our case we first calculated the standard deviation σ of raw20
EMG, and then calculated the times ti for every consecutive crossings of the21
EMG amplitude above some multiple γσ of σ and below -γσ using γ = 2.5.22
From this array ti we get the turns per time unit by forming its histogram23
whose time-resolution ∆t will consequently depend on the number of bins B24
and the duration T of the measurement (40 s in our case), ∆t = T/B. Thus,25
for T = 40 s and B = 80 we get a time resolution of 500 ms.26
As a final method we have also calculated the (complex) coherence, which for27
two time series x and y is here defined by,28
Coh(x, y)(f) =〈x⋆(f)y(f)〉
√
〈|x(f)|2〉√
〈|y(f)|2〉(12)
at the frequency f with 〈. . . 〉 denoting a statistical averaging. In our case the29
averaging was obtained by dividing the time series into sections of 10 sec-30
7
onds (corresponding to a frequency resolution of 0.1 Hz) with 50% overlap,1
calculating the Fourier-transform and their products for these sections and fi-2
nally averaging over all the sections. If x is related to y by a transfer function3
H , then Coh(x, y)(f) = H(f)/|H(f)| = exp (iφ(f)). A time shift τ can be4
calculated from the phase φ thus defined by 2πτ = dφ(f)/df . This was nu-5
merically evaluated by calculating the slope of the phase φ(f) in the frequency6
interval 0.1–1.0 Hz. Coherence is related to correlation by the fact that the7
inverse Fourier transformation of 〈x⋆(f)y(f)〉 = H(f)〈|x(f)|2〉 (in the linear8
case) produces the correlation function. In practice one has also to consider9
the influence of ”noise”.10
2.5 Data analysis, COP11
In this paper we will mostly be interested in the anterior-posterior (A/P) sway12
since this part can be quite well modeled using the human inverted pendulum13
model, and in this case the plantar flexors, whose activity is comparatively easy14
to measure, are to a large degree responsible for the motion. The COP-data15
consists of pairs of coordinates (xi, yi) with x standing for the medial-lateral16
coordinate (positive toward ”the east”), and y for the A/P COP. If we have17
N points then the ”C90” sway area A is defined by18
A =4.605π
N − 1
√
√
√
√
∑
i
(xi − 〈x〉)2∑
i
(yi − 〈y〉)2 −(
∑
i
(xi − 〈x〉)(yi − 〈y〉))2
. (13)
Here 〈x〉 =∑
i xi/N , etc. This particular definition of sway area is motivated19
by the fact that, if the variables x and y are Gaussian, then about 90% of the20
COP-points will lie inside an ellipse (the 90% confidence region) with an area21
A. The coordinates x and y are expressed in units of mm and the area in units22
of mm2. For the perturbation test data we dropped the first 10 seconds and23
used only the remaining 30 seconds of the ”recovery” phase for computing the24
sway area.25
While sway area is a space/time based parameter there is an S-parameter [22]26
based on the power spectrum of COP in the band 1 - 10 Hz. This is obtained27
by fitting the power spectrum of A/P COP (or M/L COP) to a power in terms28
of the frequency f ,29
|y(t)|2 ∝ 1
fS(f in the interval 1 - 10 Hz), (14)
8
where y denotes the Fourier-transform of A/P COP data y. A large S-parameter1
indicates that the high frequency components are suppressed.2
3 Results3
3.1 Sway area, QS-case4
One of our initial purposes of the force plate measurements was to obtain5
further data in order to test how various sway-parameters could reveal possible6
MS vs ”normal” differences. EMG-measurements were added in the hope that7
they would shed light on the muscular dynamics during quiet and disturbed8
standing. In the case of MS, which afflicts the central nervous system (CNS)9
by local degeneration of the myelin sheath (demyelation), the impoverished10
neural transduction properties (e.g. lower conduction velocities) suggest that11
the balance feedback control may be impaired. This is indicated by Fig.1 giving12
an overview of the test results showing the sway area with six QS-trials per13
participant in an alternating order EO-EC-EO . . . beginning with the sets by14
the four controls (1–4), followed by six MS-participants (5–10). Thus there are15
10 × 6 = 60 trials in all displayed. For the set 1 (a control participant) the16
results makes it look like it could belong to the MS-group while the set 6 (an17
MS-participant) might be classified as ”normal”. One may note that (control)18
participant 1 had the highest BMI-value and also reported poor eyesight, while19
MS-participant 6 had been diagnosed with MS only a year before. One peculiar20
feature that sets off the MS-group is that the EC-area is always larger than the21
EO-area for consecutive trials. This is in particular true for MS-participant 622
but not for control 1. On the group level the average eyes closed (EC) sway23
area for controls and the MS-group are 165 ± 107 mm2 (control, EC) and 63324
± 281 mm2 (MS, EC). The ratio between the average values is thus around25
3.8, a statistically significant difference on the group level. If we compute the26
average sway area for each person and for the QS/EC condition, and apply27
the Wilcoxon’s rank test [17, p.496] for the MS and the control groups, then28
their area distributions are found to be different with p < 0.01.29
3.2 Sway area, perturbed case30
The sway area was calculated for the perturbation tests by dropping the first 1031
seconds of the data; thus, only the ”recovery” phase is included. The perturba-32
tion tests show an even greater difference between the controls and MS-group33
(see Fig. 2). The medians of the sway area are 105 mm2 (control) and 691 mm234
(MS) with a ratio 1:6.6. An interesting feature is that for the MS-participants35
9
5, 7, 8 and 10 the sway area increases with each perturbation. We may note1
that the MS-participant 9 had an exceptional long break (5 min) between the2
first and the second perturbation which may have contributed to a smaller3
sway area in the second trial. The MS-participant 6 who shows a reverse4
trend was also the only MS-participant not reporting any fatigue problems.5
We mention these observations because an increase of sway area during re-6
peated perturbations tests could provide a basis for a potential neuro-muscular7
Fatiguability Index applicable to MS. Such an Index could be of interest in8
early detection or assessment of MS-progression [23, 4]. Besides fatigue one9
has also to reckon with another possible contributing factors; the fact that in10
neurogenic diseases the neuro-muscular system may have problems to adapt11
to, and anticipate, perturbations.12
The QS and perturbation sway area results indicate a significant difference13
in the balancing ability between the controls and the MS-group which raises14
the question whether a corresponding ”intrinsic” difference can be seen in the15
EMG-data. We may also note that counteracting the weight pulling, using16
dorsal flexion, was not the typical strategy. The tibialis was mostly quiet – see17
Fig.3 which shows a section of data before and after the perturbation. Instead18
the participants seemed to lean forward and let gravity do the job.19
3.3 EMG vs COP20
The A/P COP-y is almost proportional to the torque T vis-a-vis the ankle21
joints (in the sagittal plane), and thus the muscular force, since we have ac-22
cording to the human inverted pendulum model [10],23
T = yFz + ζFy ≈ ymg + ζmY ∼ ymg. (15)
Here Fz denotes the total vertical ground reaction force (GRF) (deviates from24
the weight mg of the person by less than 1% in the case of QS), Fy is the25
GRF in the y-direction (which by Newton’s equation is equal to mY where26
Y is the center-of-gravity coordinate of the person along the y-direction), and27
ζ is the distance of the ankle joint from the force plate (around 8 cm). As28
indicated the term ymg usually dominates the sum in Eq.(15). The reason is29
that y (the position of COP measured from the ankle joints in the anterior30
direction) is a positive quantity due to a forward leaning position during QS31
with an average value typically around 5 cm, while the magnitude of the32
acceleration (around the order of 1/100–1/10 m s−2) is much less than the33
gravitational acceleration g ( ≈ 9.81 m s−2). From this we may expect – since34
EMG correlates with muscular force – that the EMG measured from plantar35
flexors should correlate with A/P COP. In fact, in many instances there is36
10
a good resemblance between the A/P COP and the GA-EMG envelope as1
demonstrated by Fig.4. The EMG-envelope is calculated using the BW0-filter2
Eq.(1–5) as described above, with the contributions from both legs summed,3
and the result plotted setting the ”calibration constant” equal to 1 (”1 mm4
per µV”). If we enlarge a section of the figure we can see (Fig.5) that there is a5
systematic time shift between A/P COP and the GA-EMG envelope which in6
this case is somewhere in the range of 250–300 ms. This time shift corresponds7
to the time τ in Eq.(6). In Fig.4 we have included the EMG-turns which is also8
seen to reflect the overall pattern of the A/P COP. However, the EMG-turns9
are somewhat problematic to use for time shift calculations because of the10
low time resolution – if one increases the time resolution one tends to loose in11
terms of correlation with A/P COP.12
3.3.1 Time shifts13
We have calculated the correlations and the time shift for all trials, including14
the perturbation trials, making 10 × 9 = 90 trials in all. The results are15
presented in Figs.6-7. As can been seen the GA-EMG vs A/P COP correlation16
stays, with a few exceptions, within the range 80%–100%, while the time17
shift is in the range 250–350 ms. The ”anomalies” in cases of trials nos. 7618
and 78 (corresponding time shifts go ”through the roof”) seem to be due to19
some limitation of the algorithm rather than a lack of an EMG-COP relation.20
(Indeed, plotting the A/P COP vs the GA-EMG envelope, delayed by 320 ms21
– which was found to maximize the correlation for trial no. 78 – we found22
that the points tend to cluster in two groups instead of a single one. This23
contributes to the overall low correlation value though the curves have quite24
similar shapes.) Calculating the average correlation and time shifts excluding25
the two ”anomalous” cases we get 283 ± 43 ms (shift) and 85.5 ± 8.4%26
(correlation). Calculating the time shift separately for the groups we get 29427
± 43 ms (MS) and 266 ± 36 ms (controls). (If we calculate the average time28
shift for each person and apply the Wilcoxon’s rank test to these values then29
the MS and control distributions are deemed to be significantly different on30
the level p = 0.03.) In the case we use fc = 2.5 Hz in the BW0-filter instead31
of fc = 1 Hz the average time shift and correlation (MS + control) become32
236 ± 36 ms and 77.2 ± 9.4%; that is, a decreased correlation, and the time33
shift value no longer relates well to 1/πfc (= 127 ms).34
We have also made calculations using the CRIT2 filter Eq.(7) with fc = 1 Hz35
resulting in the correlation 78.5 ± 12.2% and time shift 22.6 ± 29.6 ms (we36
have again dropped the trial no. 78). The results are summarized in the Table37
2. The comparatively small residual time shift when using the CRIT2-filter38
Eq.(7) shows that it can account for a significant part of the time shift between39
A/P COP and GA-EMG. Tuning the cut-off frequency 10% downwards to40
0.9 Hz reduces the average shift discrepancy still further as shown by the41
11
table. The table also gives results of calculating (again dropping trial no. 78)1
with the RMS-filter. The window T = 285 ms corresponds to an ”optimal”2
approximation of the CRIT2-filter Eq.(7) with fc = 1 Hz. The time shift values3
obtained here can be contrasted with the value of 155 ± 46 ms reported by4
Masani et al [13] (n = 16, young males) for the time shift between zero phase5
filtered GA EMG and A/P COG calculated in a slightly different way (using6
fc = 4 Hz cut-off; this choice of the cut-off may account for circa 50 ms of the7
difference).8
3.3.2 EMG vs A/P COP in time domain9
Figure 8 gives an example how raw EMG (left medial gastrocnemius) may10
relate to A/P COP. (Right gastrocnemius showed in this case a weaker and11
less phasic signal.) This is from quiet standing (EO, participant 3). One can12
see how EMG ”drives” the A/P COP on the ascending side of the A/P COP13
”hills”. The A/P COP downhill parts reflect the turn-off EMD. A typical14
feature is also the burst like nature of EMG signal. In some cases one can15
find smaller amplitude recurrent burst repeating 7–10 times per second. (Kei16
Masani has made similar observation in his studies. Personal communication.).17
This was in one case even found in the RF-EMG though its EMG otherwise18
did exhibit no phasic activity.19
3.3.3 Coherence20
We have applied coherence calculation for A/P COP and GA EMG to the21
whole data set. In the first case we summed rectified EMG (as usual always22
subtracting the mean value first) from left and right GA producing an average23
coherence with A/P COP of the magnitude 80 ± 8% (range 56–93%) and a24
time shift (from the slope of the phase in the 0.1–1.0 Hz band) of 242 ± 6925
ms (range 94–430 ms). In a second case we summed the EMG envelopes of26
left and right GA based on the BW0 filter (1 Hz) which produced an average27
coherence with A/P COP of the magnitude 85 ± 7% (range 67–95%) and a28
time shift of 233 ± 62 ms (range 115–441 ms). Thus the average coherence29
time shift differs by ca 40–50 ms from the correlation time shift based on30
the BW0-filter. In general the magnitude of the coherence was around 80–31
90% in the frequency band 0.1–1.5 Hz while it for higher frequencies dropped32
markedly. These results demonstrate again that the major dynamic activity33
takes place around 1 Hz or below during quiet standing.34
12
4 Discussion1
4.1 EMG-COP time shift2
We have found the BW0-filter Eq.(1-5) to be an efficient filter for calculating3
an EMG-envelope which correlates fairly well with the torque in the quiet and4
perturbed standing cases using EMG from gastrocnemius. In combination with5
COP-data it can be used for determining the phase shift and the corresponding6
time shift between COP and EMG. What does this time shift τ consists in?7
We note that a filter like BW0 is a non-causal filter which in the time domain8
corresponds to taking a weighed average (see Eq.10); thus, the filtered value9
at time t0 depend on future EMG-values at times t > t0. For this reason10
(causality) a time shift of the form Eq.(6) is necessary. Otherwise A/P COP11
(or force/torque) would depend on future EMG-values. Therefore we expect12
the τ in Eq.(6) to be of the order of the time constant tc =(√
2πfc
)−1
in13
Eq.(10). Thus far we have only talked about a mathematical model. From14
the point of interpretation a more interesting fact is that the causal second15
order filter version Eqs.(7, 8) seems to be able to partially account for time16
shift and the A/P COP; that is, it may approximate an EMG-force model.17
Assuming this then the question arises about the physiological counterparts of18
this filter (a second order linear system). Three factors that come to mind are19
latency, electromechanical delay (EMD) associated with activation dynamics,20
and muscle-tendon properties associated with contraction dynamics [7].21
4.1.1 Electromechanical delay22
The ”electromechanical delay” (EMD) sometimes refers to the turn-on time23
which is defined as the time (latency) from the onset of EMG to the onset of24
the force, which may be about the order of 10 ms as e.g. reported by Mora et al25
[14] (among other things it depends on how one defines ”onset”, see Corcos26
et al [3]). There is also a lag associated with the turn-off defined as the time27
from the cessation of EMG to the cessation of the force, and this have been28
reported to be of the order of 100 ms [25, p. 254] or 160-200 ms [9]. The turn-off29
EMD is likely to be due to the chemical inertia of the Ca++-dynamics in the30
muscle and is related to the so called ”activation dynamics” [see e.g. 2, 18, 27,31
and references therein]. The role of the turn-off EMD tail is probably enhanced32
during quiet standing because of the silence of the antagonists (dorsal flexors).33
This may be one contributing factor to why the low 1 Hz cut-off provides34
good correlation between A/P COP and filtered EMG. The EMD lag is also a35
critical component in balancing the ”human inverted pendulum” (HIP) since36
the control must be adapted to the fact that the force continues after the37
”control signal” has ceased. Note that the characteristic time (period/(2 π))38
13
for the HIP for an adult is around 300 ms. Another important factor, as already1
mentioned, is the compliance of the tendon [15, 12, 11] which implies that the2
triceps surae must control the balance in a pulsative manner since it cannot3
lock the HIP in a fixed, slightly forward leaning position.4
One rough approach, in order to understand the turn-off EMD, is to assume5
that a pulse-like signal at t = 0 induces a force (twitch) which increase with6
a time constant τ1 while at about the same time there starts a process with a7
time constant τ2 which will reduce the force increase; i.e., the twitch is of the8
form9
h(t) =(
1 − e− t
τ1
)
e− t
τ2 . (16)
The function Eq.(16) generally illustrates a process involving a force increase10
with a time constant τ1, which will saturate and then decline as the chem-11
ical components generating the force decay (or are reabsorbed) with a time12
constant τ2. One point is that Eq.(16) in many cases, for all ”practical pur-13
poses”, may be indistinguishable from a CRIT2 transfer function Eq.(8). At14
first it may seem that Eq.(8) is obtained from Eq.(16) as an approximation15
by setting a = 1/τ1 and τc = τ2; however, a best fit (in the least mean square16
sense) leads to a more complicated relation. For instance, if we have τ1 = 5017
ms and τ2 = 100 ms then the best fit of the form Eq.(8) is given by the pa-18
rameters a = 47.1 (ms)−1 and τc = 69.3 ms. Using the approximation Eq.(8)19
of Eq.(16) two different time factors are reduced to one ”twitch” time τc. This20
case illustrates the fact that the sort of parameters and values one gets depend21
on the curve-fitting method. While the fitting using Eq.(8) may suggest why22
CRIT2 transfer functions in some cases may yield good approximations for23
EMG-to-force relations. Note that Winter [25], p. 209 quotes twitch times for24
medial gastrocnemius with values in the range 40–110 ms and with a mean25
value of 79 ms (corresponding to a frequency fc = 1/(2πτc) ≈ 2 Hz).26
4.1.2 Mechanical impedance effect27
Besides the activation dynamics may we expect influence of tendon properties28
on the resulting force measured. It is not always clear whether the tendon29
effects are included in the turn-off EMD and the twitch times. Anyway it is30
of interest to try to factor out the ”visco-elastic” component. Let us consider31
some of the salient features of a simplified model. As a hypothesis, suppose the32
contractile elements generate a force Fce determined by the level of activation33
which is measured by EMG. Assume that this force is transmitted to the bone34
via the tendon generating a tendon force Ftend = Fce + KDξce which is finally35
measured as A/P COP. Here ξce denotes the length of the contractile element36
and KD a ”viscosity” parameter (due to the ”parallel viscous element” of the37
14
force-velocity relation). Assuming further that the tendon force is given by1
KP (ξ − ξ0) (a linear relation for small amplitudes), where KP is the tendon2
stiffness and ξ is the tendon length, we obtain for the lumped inverted pendu-3
lum model and small A/P sway an equation of motion of the form (dropping4
a constant term)5
Ix +(
r2KP − mgL)
x = r2KP ξce. (17)
I denotes the body moment of inertia about to the lateral axis with respect6
to the ankle joint, r is the moment arm determined by r∆θ = ∆x for a small7
change in the sway angle ∆θ and corresponding change ∆x in the muscle-8
tendon unit (MTU) length. Using these relations one obtains for the transfer9
function between Fce and Ftend in the frequency domain (ω = 2πf),10
Ftend
Fce
=KP
KP + iωKDA−1, (18)
where we have used the abbreviations,11
A = 1 +r2KP
I (ω2 + Λ), (19)
and12
Λ =mgL − r2KP
I. (20)
Similarily one obtains the relation between the force Fce and muscle length13
ξce,14
ξce
Fce
= − 1
KP A + iωKD
. (21)
These relations involve a new characteristic time τimp = KD/KP .15
In order to get a manageable approximation we may consider the isometric16
case with x approximately constant. This corresponds to setting I = ∞ (A =17
1) in Eq.(18) which then simplifies in the time domain to the transfer function18
hmt(t) =1
τimp
e− t
τimp (t > 0). (22)
15
If we compose (convolute) this with the simplified EMG-force transfer function1
Eq.(8) we get2
htot(t) =T 2
⋆
τ 2c τimp
{
e− t
τimp + e−t
τc
(
t
T⋆
− 1)}
(t ≥ 0), (23)
where 1/T⋆ = 1/τimp−1/τc. To give an example of the effect of the impedance3
term on the total transfer function, assume that τimp = 50 ms and τc = 100 ms,4
then the transfer function Eq.(8) attains maximum at t = τc while the total5
transfer function htot(t) attains maximum at around t = 160 ms. Thus, the6
”mechanical impedance” contributes to the total transfer function by delaying7
the impulse response peak (in this case by about 60 ms). The total ”twitch8
time” of 160 ms would correspond to time shift of circa 2 × 160 ms = 320 ms in9
the low frequency end (f < fc). For the CRIT2-filter twitch time corresponds10
to the time for the impulse response function to reach the peak. We have not11
made direct measurements of the impulse response function, but Fig.3 may12
give an idea of such a function. It shows the reaction to the release of the13
perturbation weight. Determining the time for the A/P COP to reach the14
peak one obtains ca 160 ms and taking its double we get a value in a rough15
agreement with shift time values of the order of 300 ms. van Zandwijk et al16
[27] report an estimated average rise time (from 10% to 90% maximum force17
level) for triceps surae twitches to 142 ms which is comparable to 160 ms18
twitch time.19
The basic theoretical framework of Eq.(17) above seems to encompass some20
of the essential elements. It is similar to Eqs.(1, 2) in [12] except that we use21
lengths instead of angles. Observe that in [12] there is no explicit use of a ve-22
locity term, but their Eq.(9), giving the stiffness K as function of frequency f ,23
implicitely assumes that the tendon force is given by an expression of the form24
(convolution) Ftend(t) =∫
k(t − u)∆ξ(u)du where ∆ξ(u) is the extension of25
the tendon. Theoretically this covers also velocity dependent terms. Returning26
to Eq.(17) we see that, given Λ > 0 (compliant tendon), it predicts an anti-27
phase relation between contraction ξce and MTU length x as experimentally28
observed [12, 11]. The positivity of Λ implies also, according to these relations,29
that one cannot observe MTU ”resonance” in the QS case in contrast to the30
cyclic ankle bending case studied by Takeshita et al [20]. However, in order to31
explain the observed GA EMG–A/P COP shift values in the range of 250–30032
ms the above models seem to require gastrocnemius twitch times in the upper33
end of the observed ranges (100 ms), but this depends also on the contribution34
from the impedance.35
16
4.2 MS and controls difference1
Using a measure such as sway-area (trace-length would also work) a signifi-2
cant difference is found between MS and controls reflecting a generally poorer3
balance for MS. Since MS affects the CNS in a complex way it is hard to point4
to a single cause behind the impairment of balance. Possible culprits could5
be an impaired vestibular system and comprimised somatosensory feedback6
since MS contributes to delayed visual, auditory and somatosensory evoked7
potentials. One has also to reckon with secondary effects on balance e.g. due8
to increased fatiguability. As suggested this effect on balance might be used9
for measuring fatiguability.10
One general idea is that impaired balance may be related to a lack of rapid11
high frequency responses. Calculating the power spectrum exponents S for our12
data (A/P COP, quiet standing, eyes closed) we got S (control) = 3.34 ± 0.6113
and S (MS) = 3.84 ± 0.58, a not significant difference though. (According14
to the Wilcoxon’s rank test we get p = 0.08 whence the MS and control S-15
distributions are ”significantly” different only on the 8% level.)16
The small difference in the time shift values between the MS (294 ± 43 ms)17
and the control (266 ± 36 ms) lends support to the view that the time shift18
mainly reflects the EMG-force relation and to a lesser extent depends on such19
factors as the feedback loop (that may be compromised in MS).20
4.3 Conclusion21
As a part of analyzing the relation between gastrocnemius EMG and the22
anterior-posterior center of pressure we have described the details of a method23
for determining their time shift. This time shift is thought to reflect the EMG-24
to-force relation and the mechanical impedance of the muscle tendon system.25
The turn-off electromechanical delay probably accounts for most of the time26
shift. It remains though to detail the neuro-muscular chain which effects the27
balance control in order to be better able to factor the time shift into iden-28
tifiable physiological components. In future experimental studies it will be29
of interest to use more diverse and larger groups of participants in order in-30
vestigate to what extent, and in what way, the time shift is a function of31
biomechanical and anthropometric parameters. A further goal is to scrutinize32
the EMG-signal for patterns in the time domain which may shed some light33
on the nature of the balance control. There are also room for improvements34
in the methodology such as to use two force plates in order to separate the35
contributions from left and right leg. Additional kinematic sensors would also36
be useful for tracking limb and trunk movements.37
17
4.4 Acknowledgments1
This work was made possible by a project on Biosignals sponsored in large2
part by the Finnish Funding Agency for Technology and Innovation, TEKES3
(www.tekes.fi). We are indebted to Noraxon Co (www.noraxon.com, AZ,4
USA) and Dr Peter Konrad (Noraxon) EMG-measurement issues. CEO Mats5
Manderbacka (Hur Co, Finland, www.hur.fi) has contributed to the project.6
We also acknowledge support from Medirex Co (Finland). Thanks to Kei7
Masani (University of Toronto, IBBME Institute) for extended discussions8
on quiet standing and feedback control. Special thanks to the participants,9
and to Ms Linnea Luokkala, secretary of the regional (Central Ostrobothnia)10
MS-society.11
References12
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5 Full Table and Figure captions5
TAB1 The electrode placements. Reference electrode placed on the left mal-6
loleus medialis.7
TAB2 Listing of the A/P COP - EMG envelope correlations and the corre-8
sponding time shifts calculated using a selection of filters and parameters.9
Fig1 Sway area for quiet standing tests for the 10 participants (1–4 controls,10
5–10 MS). The trials are in the order EO, EC, EO, . . . , with 6 trials per11
participant (EO = eyes open, EC = eyes closed). We can see that that the12
MS-group is characterized be a significantly higher sway area in general.13
Another notable feature is that for the MS-group we have always EC-area14
> EO-area for sequential trials.15
FIG2 Sway area for quiet the perturbation tests for the 10 participants (1–416
controls, 5–10 MS). Three perturbation trials per person. Again the MS-17
group has a significantly higher sway area. We also note that 5, 7, 8 and 1018
in the MS-group the area increases with every perturbation.19
FIG3 Perturbation test. Curves from bottom up: medial gastrocnemius right,20
left, right tibialis anterior, and A/P COP. Around t = 5.2 s the ankle torque21
(A/P COP) starts to react to the release of the backward pulling weight.22
FIG4 Example of recording from a quiet standing trial (participant 3). From23
bottom up: Raw EMG (in units of 10 µV) from left medial gastrocnemius,24
A/P COP, EMG envelope and EMG turns (based on a 2.5σ-threshold and25
an 80-point histogram).26
FIG5 Enlargement of a section of the previous figure showing the shift be-27
tween the GA EMG envelope and the A/P COP.28
FIG6 Correlations between A/P COP and the GA EMG envelope (where29
contributions from left and right leg are summed) for all the 90 trials, in-30
cluding the perturbation tests. There are 9 trials per participant, 6 quiet31
standing trial in alternating order EO-EC-EO . . . plus 3 perturbation tests32
(EO). Trials 1–9 by participant 1, trials 10-18 by participant 2, etc.33
FIG7 Time shifts between GA EMG envelope and A/P COP for all the 9034
trials.35
FIG8 Raw GA-EMG (left) and A/P COP during quiet standing (EO). This36
basically illustrates the correspondence between EMG and force (A/P COP).37
One observes how EMG-activity drives the A/P COP which reverberates38
after EMG goes down.39
20
6 Tables & Figures1
Muscle placement
Tibialis anterior (TA) bilateral
Gastroc. medialis (GA) bilateral
Rectus femoris (RF) bilateral
Biceps femoris (BF) right
Multifidus (MF) right
Table 1The electrode placements. Reference electrode placed on the left malloleus medialis.
Filter Correl. (%) Time shift (ms) fc (Hz)
BW0 85.5 ± 8.4 283 ± 43 1.0
BW0 77.2 ± 9.4 236 ± 36 2.5
BW0 58.2 ± 11.6 220 ± 41 10.0
CRIT2 78.5 ± 12.2 23 ± 30 1.0
CRIT2 78.8 ± 12.3 8 ± 30 0.9
RMS 60.7 ± 10.7 231 ± 40 T = 100 (ms)
RMS 72.0 ± 10.9 283 ± 49 T = 285 (ms)
RMS 73.5 ± 11.3 321 ± 67 T = 400 (ms)
Table 2Listing of the A/P COP - EMG envelope correlations and the corresponding timeshifts calculated using a selection of filters and parameters.
21
12
34
56
78
910
11M
easurem
ent/P
articipan
t
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
C90 Area(mm2)
EO
E
C
Fig. 1. Sway area for quiet standing tests for the 10 participants (1–4 controls, 5–10MS). The trials are in the order EO, EC, EO, . . . with 6 trials per participant.
22
1 2 3 4 5 6 7 8 9 10 11Measurement/Participant
0
500
1000
1500
2000
2500
3000
3500
4000
C90
Are
a(m
m2)
1. perturb.2. perturb.3. perturb.
Fig
.2.
Sw
ayar
eafo
rth
eper
turb
atio
nte
sts
for
the
10par
tici
pan
ts(1
–4co
ntr
ols,
5–10
MS).
Thre
eper
turb
atio
ntr
ials
per
par
tici
pan
t.
23
5.1
5.2
5.3
5.4
5.5
5.6
5.7
Tim
e(s)
-100
-80
-60
-40
-20 0 20 40 60 80EMG GAd, GAs, TAd( 10 V), A/P COP(mm)
Fig. 3. Perturbation test. Curves from bottom up: medial gastrocnemius right, left,right tibialis anterior, and A/P COP. Around t = 5.2 s the ankle torque (A/P COP)starts to react to the release of the backward pulling weight.
24
05
1015
2025
3035
40T
ime
(s)
-20 0 20 40 60 80EMG raw, A/P COP, EMG-env., turns
Fig. 4. Example of recording from a quiet standing trial (EO), participant 3. En-velope of EMG from left medial gastrocnemius GA compared with A/P COP. TheEMG turns based on a 2.5σ-threshold and an 80-point histogram.
25
14.0 14.3 14.6 14.9 15.2 15.5 15.8 16.1 16.4 16.7 17.0Time(s)
-7
-2
3
8
13
18
A/P
CO
P,
EM
G-e
nv.
300 ms
Fig
.5.
Enla
rgem
ent
ofa
sect
ion
ofth
epre
vio
us
figu
resh
owin
gth
esh
ift
bet
wee
nth
eG
AE
MG
enve
lope
and
the
A/P
CO
P.
26
09
1827
3645
5463
7281
90M
easurem
ent no
.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
Correlation
Fig. 6. Correlations bewteen A/P COP and the GA EMG envelope for all the 90trials, including the perturbation tests. There are 9 trials per participant, 6 quietstanding trial in alternating order EO-EC-EO . . . plus 3 perturbation tests (EO).
27
0 9 18 27 36 45 54 63 72 81 90Measurement no.
0
100
200
300
400
500T
ime
sh
ift(m
s)
Fig
.7.
Tim
esh
ifts
bet
wee
nG
AE
MG
enve
lope
and
A/P
CO
Pfo
ral
lth
e90
tria
ls.
28
23.9
24.4
24.9
25.4
25.9
26.4
Tim
e(s)
-4 1 6
Raw EMG( 25 V), A/P COP(mm)
Fig. 8. Raw GA-EMG (left) and A/P COP during quiet standing (EO). This ba-sically illustrates the correspondence between EMG and force (A/P COP). Oneobserves how EMG-activity drives the A/P COP which reverberates after EMGgoes down. 29